libFDK/include/fixpoint_math.h

   1
   2 /* -----------------------------------------------------------------------------------------------------------
   3 Software License for The Fraunhofer FDK AAC Codec Library for Android
   4
   5 © Copyright  1995 - 2013 Fraunhofer-Gesellschaft zur Förderung der angewandten Forschung e.V.
   6   All rights reserved.
   7
   8  1.    INTRODUCTION
   9 The Fraunhofer FDK AAC Codec Library for Android ("FDK AAC Codec") is software that implements
  10 the MPEG Advanced Audio Coding ("AAC") encoding and decoding scheme for digital audio.
  11 This FDK AAC Codec software is intended to be used on a wide variety of Android devices.
  12
  13 AAC's HE-AAC and HE-AAC v2 versions are regarded as today's most efficient general perceptual
  14 audio codecs. AAC-ELD is considered the best-performing full-bandwidth communications codec by
  15 independent studies and is widely deployed. AAC has been standardized by ISO and IEC as part
  16 of the MPEG specifications.
  17
  18 Patent licenses for necessary patent claims for the FDK AAC Codec (including those of Fraunhofer)
  19 may be obtained through Via Licensing (www.vialicensing.com) or through the respective patent owners
  20 individually for the purpose of encoding or decoding bit streams in products that are compliant with
  21 the ISO/IEC MPEG audio standards. Please note that most manufacturers of Android devices already license
  22 these patent claims through Via Licensing or directly from the patent owners, and therefore FDK AAC Codec
  23 software may already be covered under those patent licenses when it is used for those licensed purposes only.
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  29 2.    COPYRIGHT LICENSE
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  56 ARE GRANTED BY THIS SOFTWARE LICENSE. Fraunhofer provides no warranty of patent non-infringement with
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  60 by appropriate patent licenses.
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  62 4.    DISCLAIMER
  63
  64 This FDK AAC Codec software is provided by Fraunhofer on behalf of the copyright holders and contributors
  65 "AS IS" and WITHOUT ANY EXPRESS OR IMPLIED WARRANTIES, including but not limited to the implied warranties
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  72
  73 5.    CONTACT INFORMATION
  74
  75 Fraunhofer Institute for Integrated Circuits IIS
  76 Attention: Audio and Multimedia Departments - FDK AAC LL
  77 Am Wolfsmantel 33
  78 91058 Erlangen, Germany
  79
  80 www.iis.fraunhofer.de/amm
  81 amm-info@iis.fraunhofer.de
  82 ----------------------------------------------------------------------------------------------------------- */
  83
  84 /***************************  Fraunhofer IIS FDK Tools  **********************
  85
  86    Author(s):   M. Gayer
  87    Description: Fixed point specific mathematical functions
  88
  89 ******************************************************************************/
  90
  91 #ifndef __fixpoint_math_H
  92 #define __fixpoint_math_H
  93
  94
  95 #include "common_fix.h"
  96
  97
  98 #define LD_DATA_SCALING (64.0f)
  99 #define LD_DATA_SHIFT   6   /* pow(2, LD_DATA_SHIFT) = LD_DATA_SCALING */
 100
 101 /**
 102  * \brief deprecated. Use fLog2() instead.
 103  */
 104 FIXP_DBL CalcLdData(FIXP_DBL op);
 105
 106 void LdDataVector(FIXP_DBL *srcVector, FIXP_DBL *destVector, INT number);
 107
 108 FIXP_DBL CalcInvLdData(FIXP_DBL op);
 109
 110
 111 void     InitLdInt();
 112 FIXP_DBL CalcLdInt(INT i);
 113
 114 extern const USHORT sqrt_tab[49];
 115
 116 inline FIXP_DBL sqrtFixp_lookup(FIXP_DBL x)
 117 {
 118   UINT y = (INT)x;
 119   UCHAR is_zero=(y==0);
 120   INT zeros=fixnormz_D(y) & 0x1e;
 121   y<<=zeros;
 122   UINT idx=(y>>26)-16;
 123   USHORT frac=(y>>10)&0xffff;
 124   USHORT nfrac=0xffff^frac;
 125   UINT t=nfrac*sqrt_tab[idx]+frac*sqrt_tab[idx+1];
 126   t=t>>(zeros>>1);
 127   return(is_zero ? 0 : t);
 128 }
 129
 130 inline FIXP_DBL sqrtFixp_lookup(FIXP_DBL x, INT *x_e)
 131 {
 132   UINT y = (INT)x;
 133   INT e;
 134
 135   if (x == (FIXP_DBL)0) {
 136     return x;
 137   }
 138
 139   /* Normalize */
 140   e=fixnormz_D(y);
 141   y<<=e;
 142   e  = *x_e - e + 2;
 143
 144   /* Correct odd exponent. */
 145   if (e & 1) {
 146     y >>= 1;
 147     e ++;
 148   }
 149   /* Get square root */
 150   UINT idx=(y>>26)-16;
 151   USHORT frac=(y>>10)&0xffff;
 152   USHORT nfrac=0xffff^frac;
 153   UINT t=nfrac*sqrt_tab[idx]+frac*sqrt_tab[idx+1];
 154
 155   /* Write back exponent */
 156   *x_e = e >> 1;
 157   return (FIXP_DBL)(LONG)(t>>1);
 158 }
 159
 160
 161
 162 FIXP_DBL sqrtFixp(FIXP_DBL op);
 163
 164 void InitInvSqrtTab();
 165
 166 FIXP_DBL invSqrtNorm2(FIXP_DBL op, INT *shift);
 167
 168 /*****************************************************************************
 169
 170     functionname: invFixp
 171     description:  delivers 1/(op)
 172
 173 *****************************************************************************/
 174 inline FIXP_DBL invFixp(FIXP_DBL op)
 175 {
 176     INT tmp_exp ;
 177     FIXP_DBL tmp_inv = invSqrtNorm2(op, &tmp_exp) ;
 178     FDK_ASSERT((31-(2*tmp_exp+1))>=0) ;
 179     return ( fPow2Div2( (FIXP_DBL)tmp_inv ) >> (31-(2*tmp_exp+1)) ) ;
 180 }
 181
 182
 183
 184 #if defined(__mips__) && (__GNUC__==2)
 185
 186 #define FUNCTION_schur_div
 187 inline FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count)
 188 {
 189   INT result, tmp ;
 190    __asm__ ("srl %1, %2, 15\n"
 191             "div %3, %1\n" : "=lo" (result)
 192                            : "%d" (tmp), "d" (denum) ,  "d" (num)
 193                            : "hi" ) ;
 194   return result<<16 ;
 195 }
 196
 197 /*###########################################################################################*/
 198 #elif defined(__mips__) && (__GNUC__==3)
 199
 200 #define FUNCTION_schur_div
 201 inline FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count)
 202 {
 203   INT result, tmp;
 204
 205    __asm__ ("srl  %[tmp], %[denum], 15\n"
 206             "div %[result], %[num], %[tmp]\n"
 207             : [tmp] "+r" (tmp), [result]"=r"(result)
 208             : [denum]"r"(denum), [num]"r"(num)
 209             : "hi", "lo");
 210   return result << (DFRACT_BITS-16);
 211 }
 212
 213 /*###########################################################################################*/
 214 #elif defined(SIMULATE_MIPS_DIV)
 215
 216 #define FUNCTION_schur_div
 217 inline FIXP_DBL schur_div(FIXP_DBL num, FIXP_DBL denum, INT count)
 218 {
 219     FDK_ASSERT (count<=DFRACT_BITS-1);
 220     FDK_ASSERT (num>=(FIXP_DBL)0);
 221     FDK_ASSERT (denum>(FIXP_DBL)0);
 222     FDK_ASSERT (num <= denum);
 223
 224     INT tmp = denum >> (count-1);
 225     INT result = 0;
 226
 227     while (num > tmp)
 228     {
 229         num -= tmp;
 230         result++;
 231     }
 232
 233     return result << (DFRACT_BITS-count);
 234 }
 235
 236 /*###########################################################################################*/
 237 #endif /* target architecture selector */
 238
 239 #if !defined(FUNCTION_schur_div)
 240 /**
 241  * \brief Divide two FIXP_DBL values with given precision.
 242  * \param num dividend
 243  * \param denum divisor
 244  * \param count amount of significant bits of the result (starting to the MSB)
 245  * \return num/divisor
 246  */
 247 FIXP_DBL schur_div(FIXP_DBL num,FIXP_DBL denum, INT count);
 248 #endif
 249
 250
 251
 252 FIXP_DBL mul_dbl_sgl_rnd (const FIXP_DBL op1,
 253                           const FIXP_SGL op2);
 254
 255 /**
 256  * \brief multiply two values with normalization, thus max precision.
 257  * Author: Robert Weidner
 258  *
 259  * \param f1 first factor
 260  * \param f2 secod factor
 261  * \param result_e pointer to an INT where the exponent of the result is stored into
 262  * \return mantissa of the product f1*f2
 263  */
 264 FIXP_DBL fMultNorm(
 265         FIXP_DBL f1,
 266         FIXP_DBL f2,
 267         INT *result_e
 268         );
 269
 270 inline FIXP_DBL fMultNorm(FIXP_DBL f1, FIXP_DBL f2)
 271 {
 272   FIXP_DBL m;
 273   INT e;
 274
 275   m = fMultNorm(f1, f2, &e);
 276
 277   m = scaleValueSaturate(m, e);
 278
 279   return m;
 280 }
 281
 282 /**
 283  * \brief Divide 2 FIXP_DBL values with normalization of input values.
 284  * \param num numerator
 285  * \param denum denomintator
 286  * \return num/denum with exponent = 0
 287  */
 288 FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom, INT *result_e);
 289
 290 /**
 291  * \brief Divide 2 FIXP_DBL values with normalization of input values.
 292  * \param num numerator
 293  * \param denum denomintator
 294  * \param result_e pointer to an INT where the exponent of the result is stored into
 295  * \return num/denum with exponent = *result_e
 296  */
 297 FIXP_DBL fDivNorm(FIXP_DBL num, FIXP_DBL denom);
 298
 299 /**
 300  * \brief Divide 2 FIXP_DBL values with normalization of input values.
 301  * \param num numerator
 302  * \param denum denomintator
 303  * \return num/denum with exponent = 0
 304  */
 305 FIXP_DBL fDivNormHighPrec(FIXP_DBL L_num, FIXP_DBL L_denum, INT *result_e);
 306
 307 /**
 308  * \brief Calculate log(argument)/log(2) (logarithm with base 2). deprecated. Use fLog2() instead.
 309  * \param arg mantissa of the argument
 310  * \param arg_e exponent of the argument
 311  * \param result_e pointer to an INT to store the exponent of the result
 312  * \return the mantissa of the result.
 313  * \param
 314  */
 315 FIXP_DBL CalcLog2(FIXP_DBL arg, INT arg_e, INT *result_e);
 316
 317 /**
 318  * \brief return 2 ^ (exp * 2^exp_e)
 319  * \param exp_m mantissa of the exponent to 2.0f
 320  * \param exp_e exponent of the exponent to 2.0f
 321  * \param result_e pointer to a INT where the exponent of the result will be stored into
 322  * \return mantissa of the result
 323  */
 324 FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e, INT *result_e);
 325
 326 /**
 327  * \brief return 2 ^ (exp_m * 2^exp_e). This version returns only the mantissa with implicit exponent of zero.
 328  * \param exp_m mantissa of the exponent to 2.0f
 329  * \param exp_e exponent of the exponent to 2.0f
 330  * \return mantissa of the result
 331  */
 332 FIXP_DBL f2Pow(const FIXP_DBL exp_m, const INT exp_e);
 333
 334 /**
 335  * \brief return x ^ (exp * 2^exp_e), where log2(x) = baseLd_m * 2^(baseLd_e). This saves
 336  *        the need to compute log2() of constant values (when x is a constant).
 337  * \param ldx_m mantissa of log2() of x.
 338  * \param ldx_e exponent of log2() of x.
 339  * \param exp_m mantissa of the exponent to 2.0f
 340  * \param exp_e exponent of the exponent to 2.0f
 341  * \param result_e pointer to a INT where the exponent of the result will be stored into
 342  * \return mantissa of the result
 343  */
 344 FIXP_DBL fLdPow(
 345         FIXP_DBL baseLd_m,
 346         INT baseLd_e,
 347         FIXP_DBL exp_m, INT exp_e,
 348         INT *result_e
 349         );
 350
 351 /**
 352  * \brief return x ^ (exp * 2^exp_e), where log2(x) = baseLd_m * 2^(baseLd_e). This saves
 353  *        the need to compute log2() of constant values (when x is a constant). This version
 354  *        does not return an exponent, which is implicitly 0.
 355  * \param ldx_m mantissa of log2() of x.
 356  * \param ldx_e exponent of log2() of x.
 357  * \param exp_m mantissa of the exponent to 2.0f
 358  * \param exp_e exponent of the exponent to 2.0f
 359  * \return mantissa of the result
 360  */
 361 FIXP_DBL fLdPow(
 362         FIXP_DBL baseLd_m, INT baseLd_e,
 363         FIXP_DBL exp_m, INT exp_e
 364         );
 365
 366 /**
 367  * \brief return (base * 2^base_e) ^ (exp * 2^exp_e). Use fLdPow() instead whenever possible.
 368  * \param base_m mantissa of the base.
 369  * \param base_e exponent of the base.
 370  * \param exp_m mantissa of power to be calculated of the base.
 371  * \param exp_e exponent of power to be calculated of the base.
 372  * \param result_e pointer to a INT where the exponent of the result will be stored into.
 373  * \return mantissa of the result.
 374  */
 375 FIXP_DBL fPow(FIXP_DBL base_m, INT base_e, FIXP_DBL exp_m, INT exp_e, INT *result_e);
 376
 377 /**
 378  * \brief return (base * 2^base_e) ^ N
 379  * \param base mantissa of the base
 380  * \param base_e exponent of the base
 381  * \param power to be calculated of the base
 382  * \param result_e pointer to a INT where the exponent of the result will be stored into
 383  * \return mantissa of the result
 384  */
 385 FIXP_DBL fPowInt(FIXP_DBL base_m, INT base_e, INT N, INT *result_e);
 386
 387 /**
 388  * \brief calculate logarithm of base 2 of x_m * 2^(x_e)
 389  * \param x_m mantissa of the input value.
 390  * \param x_e exponent of the input value.
 391  * \param pointer to an INT where the exponent of the result is returned into.
 392  * \return mantissa of the result.
 393  */
 394 FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e, INT *result_e);
 395
 396 /**
 397  * \brief calculate logarithm of base 2 of x_m * 2^(x_e)
 398  * \param x_m mantissa of the input value.
 399  * \param x_e exponent of the input value.
 400  * \return mantissa of the result with implicit exponent of LD_DATA_SHIFT.
 401  */
 402 FIXP_DBL fLog2(FIXP_DBL x_m, INT x_e);
 403
 404 /**
 405  * \brief Add with saturation of the result.
 406  * \param a first summand
 407  * \param b second summand
 408  * \return saturated sum of a and b.
 409  */
 410 inline FIXP_SGL fAddSaturate(const FIXP_SGL a, const FIXP_SGL b)
 411 {
 412   LONG sum;
 413
 414   sum = (LONG)(SHORT)a + (LONG)(SHORT)b;
 415   sum = fMax(fMin((INT)sum, (INT)MAXVAL_SGL), (INT)MINVAL_SGL);
 416   return (FIXP_SGL)(SHORT)sum;
 417 }
 418
 419 /**
 420  * \brief Add with saturation of the result.
 421  * \param a first summand
 422  * \param b second summand
 423  * \return saturated sum of a and b.
 424  */
 425 inline FIXP_DBL fAddSaturate(const FIXP_DBL a, const FIXP_DBL b)
 426 {
 427   LONG sum;
 428
 429   sum = (LONG)(a>>1) + (LONG)(b>>1);
 430   sum = fMax(fMin((INT)sum, (INT)(MAXVAL_DBL>>1)), (INT)(MINVAL_DBL>>1));
 431   return (FIXP_DBL)(LONG)(sum<<1);
 432 }
 433
 434 //#define TEST_ROUNDING
 435
 436
 437
 438
 439 /*****************************************************************************
 440
 441  array for 1/n, n=1..50
 442
 443 ****************************************************************************/
 444
 445   extern const FIXP_DBL invCount[50];
 446
 447   LNK_SECTION_INITCODE
 448   inline void InitInvInt(void) {}
 449
 450
 451 /**
 452  * \brief Calculate the value of 1/i where i is a integer value. It supports
 453  *        input values from 1 upto 50.
 454  * \param intValue Integer input value.
 455  * \param FIXP_DBL representation of 1/intValue
 456  */
 457 inline FIXP_DBL GetInvInt(int intValue)
 458 {
 459   FDK_ASSERT((intValue > 0) && (intValue < 50));
 460   FDK_ASSERT(intValue<50);
 461         return invCount[intValue];
 462 }
 463
 464
 465 #endif
 466